math question

[Deeko]

Ok...I'm doing a jacobian/change of variables question.

I determined U = XY and V = X^2 - Y^2

Now, to find the jacobian, I need to find the partials of X and Y with respect to U and V...which means I need an equation for X and Y solely in terms of U and V.

Any ideas?

 

[BA]

x=u/y
y=u/x

substitute into other equation

 

[bonkers325]

Originally posted by: Deeko
Ok...I'm doing a jacobian/change of variables question.

I determined U = XY and V = X^2 - Y^2

Now, to find the jacobian, I need to find the partials of X and Y with respect to U and V...which means I need an equation for X and Y solely in terms of U and V.

Any ideas?

the partial of U w/ respect toX is Y and the w/ respect to Y is X. so V = (partial of U w/ respect to Y)^2 - (partial of U w/ respect to X)^2

 

[Deeko]

Originally posted by: BA
x=u/y
y=u/x

substitute into other equation

ah but the problem with that is, im still left with a y in the x equation or an x in the y equation...must be X = something with no y's and
y = something with no x's

 

[andylawcc]

u = xy
v = x2 - y2

1)
u/x = y2

v = x2 - (u/x)2

urr... it doesn't work1!!!!!! damn you Newton!

 

[BA]

no, you aren't

say x=u/y
substitute into v=x^2-y^2

v=(u/y)^2-y^2

It's all v,u,and y. Just solve for y



And this is with 4 shots of SoCo in me.(I also taught algebra for the last two years)

 

[dighn]

just substitute and differentiate implicitly

 

[andylawcc]

Originally posted by: BA
no, you aren't

say x=u/y
substitute into v=x^2-y^2

v=(u/y)^2-y^2

It's all v,u,and y. Just solve for y



And this is with 4 shots of SoCo in me.(I also taught algebra for the last two years)

humm... SoCo... yummm...


anyways, when you become sober, try to "solve for y" yourself 😉